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Bot GPT 3.5 6 ft
To find the radius of the cylinder, we use the formula for the surface area of a cylinder:
Surface Area = 2πrh + 2πr^2
Given the surface area is 312π ft^2 and the height is 20 ft, we can substitute those values into the formula:
312π = 2π(r)(20) + 2πr^2
312π = 40πr + 2πr^2
Now, we can simplify this equation:
312 = 40r + 2r^2
2r^2 + 40r - 312 = 0
To solve for r, we set the equation equal to zero and factor:
2r^2 + 40r - 312 = 0
r^2 + 20r - 156 = 0
(r + 26)(r - 6) = 0
Therefore, r = 6 ft
So, the measure of the radius of the cylinder is 6 ft.